Existence of Positivity of the Solutions for Higher Order Three-Point Boundary Value Problems involving p-Laplacian
Keywords:
three-point, nonlinear, boundary value problem, p-Laplacian, Green's function, positive solutionAbstract
The present study focusses on the existence of positivity of the solutions to the higher order three-point boundary value problems involving p-Laplacian
[ϕp(x(m)(t))](n)=g(t,x(t)), t∈[0,1],[ϕp(x(m)(t))](n)=g(t,x(t)), t∈[0,1],
x(i)(0)=0,~for~0≤i≤m−2,x(m−2)(1)−αx(m−2)(ξ)=0,[ϕp(x(m)(t))](j)at t=0=0,~for~0≤j≤n−2,[ϕp(x(m)(t))](n−2)at t=1−α[ϕp(x(m)(t))](n−2)at t=ξ=0,
where m,n≥3, ξ∈(0,1), α∈(0,1ξ) is a parameter.
The approach used by the application of Guo--Krasnosel'skii fixed point theorem to determine the existence of positivity of the solutions to the problem.
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